Question

$2x ^{4} -4 x^{3} - 3x - 1 \div x - 1$​

Answer 1

$\huge\bold{\gray{\sf{Answer:}}}$

Explanation:

$2 {x}^{4} - 4 {x}^{3} - 3x - 1 \div x - 1$

We get :

$\bold{\boxed{ - 2 {x}^{2} - 4 = Remainder}}$

$\bold{\boxed{2 {x}^{3} - 2 {x}^{2} - 3 = Quotient}}$

CHECK:

$\bold{\boxed{Dividend =Divisor ×Quotient +Remainder}}$

$\bold{\red{2 {x}^{4} - 4 {x}^{3} - 3x - 1}} = (x - 1)(2 {x}^{3} - 2 {x}^{2} - 3) ( + )- 2 {x}^{2} - 4$

$= 2 {x}^{4} - 2 {x}^{3} - 3x - 2 {x}^{3} + {\cancel{2 {x}^{2} }} + 3{\cancel{ - 2 {x}^{2}}} - 4$

$={\red{ 2 {x}^{4} - 4 {x}^{3} - 3x - 1}}$

Proved✓